Why the day and night line curves, and how fast it moves

On a sphere, it is a circle

The sun is far enough away that its light arrives in parallel rays, so exactly half of Earth is lit at any moment. The boundary of that half, called the terminator, is a great circle: the largest circle you can draw on the sphere, like the equator or a meridian. Everyone on it is watching either a sunrise or a sunset.

The point directly under the sun, the subsolar point, is the centre of the lit hemisphere. The terminator is the circle 90 degrees away from it in every direction. Find the subsolar point and you have found the terminator, which is exactly how the live globe draws it: the site computes where the sun is overhead using the standard NOAA solar equations, then shades everything more than 90 degrees from that point.

Why it leans with the seasons

Earth's axis is tilted 23.44 degrees from its orbit, so the subsolar point is not fixed on the equator. It drifts north to the Tropic of Cancer at the June solstice, back to the equator at the September equinox, south to the Tropic of Capricorn in December, and back again in March. The seasons page shows its latitude live.

Because the terminator is always 90 degrees from the subsolar point, it tilts as the sun does. At an equinox the subsolar point is on the equator, the terminator runs through both poles, and every place on Earth gets twelve hours of daylight. In June the circle is tipped so that it misses the North Pole entirely: everything north of the Arctic Circle is inside the lit half all day, and everything south of the Antarctic Circle is in darkness all day.

Flatten that tilted circle onto a rectangular map and it becomes the familiar wave. In June the curve bulges northward over the night side, so the northern hemisphere's share of the lit side is larger; in December it bulges the other way. At the equinoxes the wave flattens into a straight vertical line.

How fast it moves

Earth's circumference at the equator is about 40,075 kilometres and it turns once in 24 hours, so the terminator sweeps westward across the equator at roughly 1,670 kilometres per hour, faster than the speed of sound. At 60 degrees latitude the circle of latitude is half as long, so the line moves at about 835 kilometres per hour there. At the poles it barely moves at all.

That speed is why sunset is quick in the tropics. The sun's altitude changes by 15 degrees per hour at the equator, so the 6-degree band of civil twilight takes about 24 minutes to pass over a point, and the band itself is roughly 670 kilometres wide on the ground. Near the poles the band is spread over a vast area and takes hours to pass, which the twilight guide covers in detail.

Reading the globe

On the home page globe, night is not a hard-edged shadow. Each pixel is shaded by the sun's actual altitude at that point, so the terminator fades through civil, nautical and astronomical twilight instead of stopping dead, and a warm band marks where the sun is on the horizon. Drag the time scrubber and the whole pattern rotates westward at the real rate, 15 degrees of longitude for every hour.

The yellow glow is the subsolar point. Click it and the panel reports which country or ocean the sun is directly over, the season implied by its latitude, and which cities are on the sunrise and sunset line at that moment. The date line is a different boundary altogether: it is fixed on the map, while the terminator circles the planet once a day.

See it on the site

• Live day and night globeDrag the time scrubber to watch the terminator move at its real speed.
• Equinoxes and solsticesThe subsolar latitude live, and the instants it reaches the tropics and the equator.
• Sunrise and sunsetThe moment the line passes any listed city, with the twilight bands either side.